Internal problem ID [1567]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 9 Introduction to Linear Higher Order Equations. Section 9.3. Undetermined
Coefficients for Higher Order Equations. Page 495
Problem number: section 9.3, problem 70.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime \prime }-y^{\prime \prime }-y^{\prime }+y+{\mathrm e}^{-x} \left (4-8 x \right )=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 2, y^{\prime }\relax (0) = 0, y^{\prime \prime }\relax (0) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 23
dsolve([diff(y(x),x$3)-1*diff(y(x),x$2)-1*diff(y(x),x)+1*y(x)=-exp(-x)*(4-8*x),y(0) = 2, D(y)(0) = 0, (D@@2)(y)(0) = 0],y(x), singsol=all)
\[ y \relax (x ) = \left (x^{2}+x +1\right ) {\mathrm e}^{-x}-\left (x -1\right ) {\mathrm e}^{x} \]
✓ Solution by Mathematica
Time used: 0.072 (sec). Leaf size: 26
DSolve[{y'''[x]-1*y''[x]-1*y'[x]+1*y[x]==-Exp[-x]*(4-8*x),{y[0]==2,y'[0]==0,y''[0]==0}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{-x} \left (x^2+x+1\right )-e^x (x-1) \\ \end{align*}